As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

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Orbital angular momentum: origins, behavior and applications

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

Helical-wavefront laser beams produced with a spiral phaseplate

Laser beams that contain phase singularities can be generated with computer-generated holograms, which in the simplest case have the form of spiral Fresnel zone plates.

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Generation of optical phase singularities by computer-generated holograms.

The various arguments for introducing optical interconnections to silicon CMOS chips are summarized, and the challenges for optical, optoelectronic, and integration technologies are discussed. Optics could solve many physical problems of interconnects, including precise clock distribution, system synchronization (allowing larger synchronous zones, both on-chip and between chips), bandwidth and density of long interconnections, and reduction of power dissipation. Optics may relieve a broad range of design problems, such as crosstalk, voltage isolation, wave reflection, impedence matching, and pin inductance. It may allow continued scaling of existing architectures and enable novel highly interconnected or high-bandwidth architectures. No physical breakthrough is required to implement dense optical interconnects to silicon chips, though substantial technological work remains. Cost is a significant barrier to practical introduction, though revolutionary approaches exist that might achieve economies of scale. An Appendix analyzes scaling of on-chop global electrical interconnects, including line inductance and the skin effect, both of which impose significant additional constraints on future interconnects.

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Rationale and challenges for optical interconnects to electronic chips

Polarization-state selection, polarization-state dynamics, and polarization switching of a quantum-well vertical-cavity surface-emitting laser (VCSEL) for the lowest order transverse spatial mode of the laser is explored using a recently developed model that incorporates material birefringence, the saturable dispersion characteristic of semiconductor physics, and the sensitivity of the transitions in the material to the vector character of the electric field amplitude. Three features contribute to the observed linearly polarized states of emission: linear birefringence, linear gain or loss anisotropies, and an intermediate relaxation rate for imbalances in the populations of the magnetic sublevels. In the absence of either birefringence or saturable dispersion, the gain or loss anisotropies dictate stability for the linearly polarized mode with higher net gain; hence, switching is only possible if the relative strength of the net gain for the two modes is reversed. When birefringence and saturable dispersion are both present, there are possibilities of bistability, monostability, and dynamical instability, including switching by destabilization of the mode with the higher gain to loss ratio in favor of the weaker mode. We compare our analytical and numerical results with recent experimental results on bistability and switchings caused by changes in the injection current and changes in the intensity of an injected optical signal.

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Polarization properties of vertical-cavity surface-emitting lasers

We analyze the interaction and the competition of a set of transverse cavity modes, which belong to a frequency-degenerate family. The laser turns out to be able to realize several different stationary spatial patterns, which differ in the transverse configuration of the intensity or of the field and are met by varying the values of the control parameters. A striking feature that emerges in almost all steady-state patterns is the presence of dark points, in which both the real and the imaginary part of the electric field vanish and such that, if one covers a closed loop around one of these points, the field phase changes by a multiple of 2\ensuremath{\pi}, which corresponds to the topological charge of the point. We show in detail the analogy of these phase singularities to the vortex structures well known in such fields as, for example, hydrodynamics, superconductivity, and superfluidity. In our case, at steady state, these singularities are arranged in the form of regular crystals, nd the equiphase lines of the field exhibit a notable similarity to the field lines of the electrostatic field generated by a corresponding set of point charges. We analyze in detail the patterns that emerge in the cases 2p+l=2 and 2p+l=3, where p and l are the radial and angular modal indices, respectively, and we compare the results with the experimental observations obtained from a ${\mathrm{Na}}_{2}$ laser. The observed patterns agree in detail with those found by theory; in particular, they exhibit the predicted phase singularities in each pattern. The transitions from one pattern to another, that one observes under variation of the control parameters, basically agree with those predicted by theory.

Transverse laser patterns. I. Phase singularity crystals

Spatial Soliton Pixels in Semiconductor Devices

We consider a semiconductor microcavity driven by a coherent and stationary holding beam, in two distinct configurations. In the first, no carriers are injected in the multiple-quantum-well structure and the optical nonlinearity is governed by an excitonic resonance. The second corresponds to that of a vertical-cavity surface-emitting laser kept slightly below threshold. We describe both configurations using a unified model that includes both field diffraction and carrier diffusion. We calculate numerically both the time evolution and the stationary profile of the solitonic solutions, using a generalization of the radial integration technique introduced by Firth and Scroggie [Phys. Rev. Lett. 76, 1623 (1996)]. We analyze the instability that forms spatial patterns and especially cavity spatial solitons. We predict the existence of these solitons in various parametric domains for both configurations. We demonstrate that these results are independent of the periodic boundary conditions used in the simulations. We show that, introducing a simple phase modulation in the holding beam, one can eliminate the motions of solitons that arise from noise and from amplitude gradients. The solitons are robust with respect to parametric variations, to carrier diffusion, and even to some amount of self-defocusing. This picture points to the possibility of realizing arrays of solitonic pixels using semiconductor microresonators.

Spatial solitons in semiconductor microcavities

Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

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Franco Prati

Papers

Polarization properties of vertical-cavity surface-emitting lasers

Transverse laser patterns. I. Phase singularity crystals

Spatial Soliton Pixels in Semiconductor Devices

Spatial solitons in semiconductor microcavities

Nonlinear Optical Systems